The primary objective of this open-label, controlled, randomized study is to identify whether a single subcutaneous dose of PROCRIT, epoetin alpha, given weekly is as effective as the standard three times per week dose (150 IU/kg) for the treatment of anemia in cancer patients receiving platinum-containing chemotherapy. The open label design consists of 6 groups. One group does not receive any PROCRIT. Group 2 receives standard 3x/ week dosing. Then 4 groups of once a week dosing at 300, 450, 600, and 900 IU/kg/wk . The major endpoint is the proportion of patients achieving an increase of hemoglobin by >2 g/dl.